France, Netherlands, Germany, and the U.K. are all countries with large and growing immigrant populations. Seeing their countries 'taken over' by foreigners, people vote for parties promising to put a stop to it. Unfortunately, there are no pro-EU parties making those promises. Quite the opposite - they prefer to chastise their people for not wanting their countries to irreversibly change. So that's how you end up with this mess - I don't think prodding by the Americans had much to do with it.